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CFD Modeling of Heat and Moisture Transfer on a 2-D Model of a Beef Leg

CFD Modeling of Heat and Moisture Transfer on a 2-D Model of a Beef Leg. Francisco J. Trujillo and Q. Tuan Pham University of New South Wales Sydney 2052, Australia. Objective 1.

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CFD Modeling of Heat and Moisture Transfer on a 2-D Model of a Beef Leg

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  1. CFD Modeling of Heat and Moisture Transfer on a 2-D Model of a Beef Leg Francisco J. Trujillo and Q. Tuan Pham University of New South Wales Sydney 2052, Australia 2003 International Congress of Refrigeration, Washington, D.C., August 17-22, 2003

  2. Objective 1 • To report on problems encountered while trying to model simultaneous heat and mass transfer in both air and solid phases during beef carcass chilling, using the CFD package FLUENT 6.0 2003 International Congress of Refrigeration, Washington, D.C., August 17-22, 2003

  3. Objective 2 • To report preliminary results on a simple shape 2003 International Congress of Refrigeration, Washington, D.C., August 17-22, 2003

  4. Why we must model heat and mass transfer During chilling of beef carcasses, cooling and evaporation influences • meat temperature • surface water activity • microbial growth • weight loss • tenderness • other quality factors 2003 International Congress of Refrigeration, Washington, D.C., August 17-22, 2003

  5. In the solid Change = Diffusion • where  may be • temperature • moisture concentration Transport equations In the air Change = Convection + Diffusion + Source • where  may be • 1 (continuity) • velocity components u, v • turbulent kinetic energy k • turbulent dissipation rate  • temperature • water vapour concentration 2003 International Congress of Refrigeration, Washington, D.C., August 17-22, 2003

  6. Turbulence model k-model: effective viscosity calculated from turbulent intensity k and turbulent dissipation  RNG modification: RNG (Re-Normalization Group) : includes analytical formula for effective viscosity that is valid across the full range of flow conditions, from low to high Reynolds numbers Enhanced wall treatment • Viscosity effects near wall is completely resolved all the way to the viscous sub-layer (y+ 1)using very fine mesh. • Enhanced wall functions: smoothly blend linear (laminar) and logarithmic (turbulent) laws-of-the-wall. 2003 International Congress of Refrigeration, Washington, D.C., August 17-22, 2003

  7. Why is it difficult to model simultaneous heat and mass transfer in meat • Moisture diffusion is mostly near the surface, while heat conduction takes place over the whole body • Due to steep moisture profile near surface, a very fine mesh is required 2003 International Congress of Refrigeration, Washington, D.C., August 17-22, 2003

  8. Problem related to FLUENT’s capabilities In the meat, the heat and mass transfer could not be solved using FLUENTs standard heat and mass transfer equations because: • FLUENT cannot solve mass transfer equation in a solid. Thus the meat had to be defined as a “fluid” phase. • Once the meat was defined as a fluid, FLUENT requires the physical properties (cp, , D, k, ) be the same in all parts of the solution domain (i.e. both air and meat phases are modelled as the same substance). • Since these properties were in fact different in the two phases, new field variables must be defined and solved in the meat. • FLUENT6.0 “ready-made” boundary conditions of the mass transport equations can only be zero flux or a fixed value. 2003 International Congress of Refrigeration, Washington, D.C., August 17-22, 2003

  9. Details of special FLUENT procedures • Define new field variables called UDS (User Defined Scalars) which represent the moisture concentration and temperature in the meat. These new fields must be tied to those in the air using equilibrium and conservation laws... 2003 International Congress of Refrigeration, Washington, D.C., August 17-22, 2003

  10. Write user-defined functions in C++ to calculate the boundary condition of mass transfer equation in meat: • (the mass flux at the meat surface is calculated from the water vapour gradient in the air cell next to the surface) UDF1: B.c. for mass transfer in meat: 2003 International Congress of Refrigeration, Washington, D.C., August 17-22, 2003

  11. (convective heat flux is calculated from T gradient in the air cell next to the surface.) (evaporative heat flux is calculated from mass flux calculated earlier) UDF2: B.c. for heat transfer in meat: • Write user-defined functions to calculate the boundary condition of heat transfer equation in meat: (the heat flux from the meat at the surface is calculated from the convective, evaporative and radiated heats), where 2003 International Congress of Refrigeration, Washington, D.C., August 17-22, 2003

  12. UDF4: B.c. for mass transfer in air: • Write user-defined functions to calculate the boundary condition of mass transfer equation in air: • where • aw(meat surface) is calculated from meat surface moisture content using measured isotherm on right • aw(air surface) is the relative humidity in the air at the interface 2003 International Congress of Refrigeration, Washington, D.C., August 17-22, 2003

  13. Write user-defined functions to calculate the boundary condition of heat transfer equation in air: UDF3: B.c. for heat transfer in air: 2003 International Congress of Refrigeration, Washington, D.C., August 17-22, 2003

  14. Solution procedure for each iteration For each time t Iterate • Solve linearized momentum equation in the air phase. • Solve energy equation in the air phase. • Solve mass equation in the air phase. • Solve turbulent kinetic energy in the air phase. • Solve eddy dissipation in the air phase. • Solve energy equation in the solid phase. • Solve mass equation in the meat phase. • Update all properties • Check convergence. until results have converged (no more change in field variables) Advance to next time t+t 2003 International Congress of Refrigeration, Washington, D.C., August 17-22, 2003

  15. CFD Grid • air side: 29033 nodes • meat side: 6487 nodes 2003 International Congress of Refrigeration, Washington, D.C., August 17-22, 2003

  16. Bound. layer detachment Impingement (stagnation point) Recirculation Results: Velocity profile 2003 International Congress of Refrigeration, Washington, D.C., August 17-22, 2003

  17. Result: Temperature profiles at 30 minutes 2003 International Congress of Refrigeration, Washington, D.C., August 17-22, 2003

  18. Result: Temperature profiles after 5 hours 2003 International Congress of Refrigeration, Washington, D.C., August 17-22, 2003

  19. Result: Moisture profiles in meat after 5 hours 2003 International Congress of Refrigeration, Washington, D.C., August 17-22, 2003

  20. Result: Moisture profiles in meat after 20 hours 2003 International Congress of Refrigeration, Washington, D.C., August 17-22, 2003

  21. Results: Temperature history Comparison of ellipse model with “equivalent” real beef leg: 2003 International Congress of Refrigeration, Washington, D.C., August 17-22, 2003

  22. Results: Temperature profile along surface Front of ellipse Back of ellipse 2003 International Congress of Refrigeration, Washington, D.C., August 17-22, 2003

  23. Results: Average surface water activity history Note surface rewetting 2003 International Congress of Refrigeration, Washington, D.C., August 17-22, 2003

  24. Results: Water activity profile along surface 2003 International Congress of Refrigeration, Washington, D.C., August 17-22, 2003

  25. Results: Moisture profile in the meat Note diffusion depth  20mm Note surface re-wetting 2003 International Congress of Refrigeration, Washington, D.C., August 17-22, 2003

  26. Results: Variation of htc and mtc along surface 2003 International Congress of Refrigeration, Washington, D.C., August 17-22, 2003

  27. How long did it take? CFD calculation is time consuming because • Grid is very fine on both sides of interface: • air side (29033 nodes): for enhanced wall treatment • meat side (6487): because of small scale of mass transfer • Must iterate at each time interval to satisfy 2 equilibrium equations and 2 flux conservation equations at meat-air interface  160 CPU hours (on a 1.5GHz Pentium 4) to simulate 20 hours of real time. 2003 International Congress of Refrigeration, Washington, D.C., August 17-22, 2003

  28. CONCLUSIONS • Even though FLUENT 6.0 is a very powerful CFD software, special techniques have to be used to deal with simultaneous heat and mass transfer in two different phases • Solution is very time-consuming - not yet practical for routine industrial calculations. • The model gave reasonable predictions of local variations in temperature, moisture and water activity 2003 International Congress of Refrigeration, Washington, D.C., August 17-22, 2003

  29. ACKNOWLEDGMENTS This work was carried out under a grant by the Australian Government via the Australian research Council. Francisco Trujillo is supported by a Postgraduate scholarship funded by the grant. 2003 International Congress of Refrigeration, Washington, D.C., August 17-22, 2003

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